The Microscopic Origin of the Pareto Law and Other Power-Law Distributions

Marco Patriarca, Els Heinsalu, Anirban Chakraborti, Kimmo Kaski

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review


Many complex systems are characterized by power-law distributions, beginning with the first historical example of the Pareto law for the wealth distribution in economic systems. In the case of the Pareto law and other instances of power-law distributions, the power-law tail can be explained in the framework of canonical statistical mechanics as a statistical mixture of canonical equilibrium probability densities of heterogeneous subsystems at equilibrium. In this picture, each subsystem interacts (weakly) with the others and is characterized at equilibrium by a canonical distribution, but the distribution associated to the whole set of interacting subsystems can in principle be very different. This phenomenon, which is an example of the possible constructive role of the interplay between heterogeneity and noise, was observed in numerical experiments of Kinetic Exchange Models and presented in the conference “Econophys-Kolkata-I”, hold in Kolkata in 2005. The 2015 edition, taking place ten years later and coinciding with the twentieth anniversary of the 1995 conference hold in Kolkata where the term “Econophysics” was introduced, represents an opportunity for an overview in a historical perspective of this mechanism within the framework of heterogeneous kinetic exchange models (see also Kinetic exchange models as D-dimensional systems in this volume). We also propose a generalized framework, in which both quenched heterogeneity and time dependent parameters can comply constructively leading the system toward a more robust and extended power-law distribution.
Original languageEnglish
Title of host publicationEconophysics and Sociophysics: Recent Progress and Future Directions
EditorsFrédéric Abergel, Hideaki Aoyama, Bikas K. Chakrabarti, Anirban Chakraborti, Nivedita Deo, Dhruv Raina, Irena Vodenska
Place of PublicationCham
Number of pages18
ISBN (Electronic)978-3-319-47705-3
ISBN (Print)978-3-319-47705-3
Publication statusPublished - 2017
MoE publication typeA3 Part of a book or another research book
EventInternational Workshop Econophys - New Delhi, India
Duration: 27 Nov 20151 Dec 2015
Conference number: 9

Publication series

NameNew economic windows
ISSN (Print)2039-411X
ISSN (Electronic)2039-4128


WorkshopInternational Workshop Econophys
Abbreviated titleEconophys
CityNew Delhi


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